Mathematics – Classical Analysis and ODEs
Scientific paper
2006-08-29
Mathematics
Classical Analysis and ODEs
39 pages
Scientific paper
The article is devoted to the investigation of smoothness of functions $f(x_1,...,x_m)$ of variables $x_1,...,x_m$ in infinite fields with non-trivial multiplicative ultra-norms, where $m\ge 2$. Theorems about classes of smoothness $C^n$ or $C^n_b$ of functions with continuous or bounded uniformly continuous on bounded domains partial difference quotients up to the order $n$ are investigated. It is proved, that from $f\circ u\in C^n({\bf K},{\bf K}^l)$ or $f\circ u\in C^n_b({\bf K},{\bf K}^l)$ for each $C^{\infty}$ or $C^{\infty }_b$ curve $u: {\bf K}\to {\bf K}^m$ it follows, that $f\in C^n({\bf K}^m,{\bf K}^l)$ or $f\in C^n_b({\bf K}^m,{\bf K}^l)$ respectively. Moreover, classes of smoothness $C^{n,r}$ and $C^{n,r}_b$ and more general in the sense of Lipschitz for partial difference quotients are considered and theorems for them are proved.
No associations
LandOfFree
Smoothness of functions global and along curves over ultra-metric fields does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Smoothness of functions global and along curves over ultra-metric fields, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Smoothness of functions global and along curves over ultra-metric fields will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-334083